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This paper concerns a method of testing equality of distribution of randomconvex compact sets and the way how to use the test to distinguish between tworealisations of general random sets. The family of metrics on the space ofdistributions of random convex compact sets is constructed using the theory ofN-distances and characteristic functions of random convex compact sets.Further, the approximation of the metrics through its finite dimensionalcounterparts is proposed, which lead to a new statistical test for testingequality in distribution of two random convex compact sets. Then, it isdescribed how to approximate a realisation of a general random set by a unionof convex compact sets, and it is shown how to determine whether tworealisations of general random sets come from the same process using theconstructed test. The procedure is justified by an extensive simulation study.

Testing equality in distribution of random convex compact sets via  theory of N-distances and its application to assessing similarity of general  random sets